The primary purpose of this study is to test the efficacy of Lisdexamfetamine in Adults With Attention Deficit Hyperactivity Disorder (ADHD) and Sluggish Cognitive Tempo (SCT). This is a placebo controlled, cross-over clinical trial of oral Lisdexamfetamine Dimesylate 30-70mg/day in adults with attention-deficit hyper-activity disorder and Sluggish Cognitive Tempo (ACT). Patients will be assigned either LDX/Placebo for 10 weeks with a two week placebo washout period.